Homogeneous nearly Kähler manifolds

Abstract

We classify six-dimensional homogeneous nearly Kähler manifolds and give a positive answer to Gray and Wolf’s conjecture: every homogeneous nearly Kähler manifold is a Riemannian 3-symmetric space equipped with its canonical almost Hermitian structure. The only four examples in dimension 6 are S3 × S3, the complex projective space ℂP3, the flag manifold